Wall-modeled large-eddy simulation based on spectral-element discretization

The continuous Galerkin spectral-element method (SEM) has long been used for high-fidelity simulations of turbulent flows, particularly for direct numerical simulations. To circumvent the usual limitations on the maximum affordable Reynolds number, wall-modeled large-eddy simulation (WMLES) using SEM has been proposed in the literature. However, existing works are confined to channel flow, and several methodological questions remain, such as numerical stability and subgrid scale modeling, when grid quality is that typical of applications. Here, WMLES is conducted using the SEM solver Nek5000, considering three flows: turbulent channel flow, a flat-plate turbulent boundary layer, and flow over the A-airfoil at near-stall conditions. Thus, we expand the assessment of WMLES-based SEM to a larger class of flow conditions, with the principal conclusion that state-of-the-art predictive accuracy can be achieved. However, further methodological improvements are needed to obtain smooth solutions on coarser grids, which are typical of WMLES. We show that established algebraic subgrid scale models (Vreman, Sigma) introduce sufficient diffusion to stabilize simulations and outperform modal filtering, yet mean turbulent viscosity profiles still exhibit spurious peaks due to velocity derivative jumps across elements. We also investigate the impact of time-averaging the velocity input to the wall model and find it to be negligible. Finally, our simulations of the A-airfoil highlight the critical need for accurately resolving the laminar region near the leading edge and developing wall models capable of detecting and handling transition.